Question

I need help with this practice problem It asks to answer (a) & (b)

Answer 1

Given series,

`\sum ^(\infty)_(n\mathop=1)((2n!)/(2^(2n)))`

a.The value of r is

`\begin{gathered} r=\lim _(n\to\infty)|(a_(n+1))/(a_n)| \\ \Rightarrow r=\lim _(n\to\infty)((2n+1)!)/(2^(2(n+1)))*(2^(2n))/((2n)!) \\ \Rightarrow r=\lim _(n\to\infty)(2(n+1))/(4)=\infty \end{gathered}`

b. Since r is infinity so the series is divergent.